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That's right, I said it, this guide has everything you need to know about AP ratios

What exactly is an Ability Power Ratio?

Here's what they are:
Some champion spells have a (+0) in the tooltip. This means that along with the damage it normally gives, it can be upgraded via ability power (AP). Here's some math to show exactly how this works:

We'll take Cho'Gath's Rupture, it has an AP ratio of 1.0, let's say we have 100 AP and rupture is lvl 5, the tooltip will say:

Mordekaiser-The Master of Metal
Mace of Spades 0.4
Creeping Death 0.2 (per second for 6 seconds, anywhere from 0.2 to 1.2)
Siphon of Destruction 0.6
Children of the Grave (life drain) 0.04%
Children of the Grave 0.75 [from the ghost]

Blitzcrank-The Great Steam Golem
Mana Shield 50% (total mana)
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It would be nice if this thread was stickied, then everyone will be able to access it
(I will keep it up-to-date).

Extremely special thanks to Bland for all the insane amount of testing he's put time into <3 U man

Special thanks to Lollerman for the AP ratio list he already assembled and testing some things.

Special thanks to Dreampod for getting me the Nidalee ratios.

Special thanks to Pinith for giving me the idea for damage over time ratios.

Special thanks goes to mermin for finding the initial Poppy ratios.

Special thanks goes to Bland for finding the initial Gragas and Pantheon ratios, as well as the Mordekaiser ratios.

Special thanks goes to Wriggle for finding initial Ezreal ratios

Special thanks goes to Emit for finding the Kennen ratios (before I even asked), and for finding the Alkali ratios

Special thanks goes to Shakodar for finding the nonexistant Garen ratios

Special thanks goes to I Got Vent for finding the Malzahar ratios

Special thanks goes to DOOMSNIPES for presenting the Kog'Maw ratios, as well as the stuff for patch v1.0.0.104

Special thanks goes to Ravenite for testing and presenting the ratios for Galio

Special thanks goes to hermeneutist for helping me clarify the guide more

I've tested Janna a bit and I believe Howling Gale is only 0.75, not 0.8.
Monsoon's healing likewise came out to 0.25 in my tests.

Alistar's Headbutt should be 1.0 exactly: I've pushed him to over 150 AP before, which means if the ratio is higher, there would have been a discrepancy between my AP value and the damage modifier on the skill tooltip. As the two values were identical....